Non-Equilibrium Thermodynamics and Its Corrections to Thermal Equilibrium

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Abstract
Non-equibrium thermodynamics is discussed by integrating the equation of motion with an initial condition on the density matrix. Using the adiabatic theorem, exact expressions for the lowest correction terms to the equilibrium thermodynamics are given. They are written in terms of the Green's functions or the generating functional of the Green's functions. Phenomenological coefficients are determined appearing in various equations of the non-equilibrium processes; the increase of the internal energy by the non-adiabatic external force, increase of the entropy for the isolated system.

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